Name Time1. Differentiate the following using the derivative rules.(a) f(x) = x3(3x2+ 1)5(6x − 7)4(b) f(x) =3 cos2(2x)x + 3 sin (2x)(c) f(x) = 3 tan3(x2)(d) f(x) =q(4x − 3)3+ x2− 1(e) f(x) =(8x3− 3x + 1)3+ 6x4+ 5 sin (3x)22. Determine the equation of the tangent line to the curve (2x + y)4− 3y + xy − 4 = 0at the point (2, −3).3. Find the points on the ellipse x2+ 2y2= 1 where the t angent line has a slope of 1.(Hint: Solve for x in terms of y wheredydx= 1.)4. (a) Determine t he equation of the tangent line to the curve x2+y2+y cos x+3x = 0at the point (0, −1).(b) Use linear approximation (the tangent line) to estimate y when x = 0.1.5. Determine the limit.(a) limx→4x2− 5x + 4x − 4(b) limh→2−x2− 3x − 2x − 2(c) limx→2+x2− 3x − 2x − 2(d) limx→∞4 − x23x2− 7x + 5(e) limx→1−|x2− 1|x − 1(f) limx→1+|x2− 1|x −
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